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4 years ago

Plot the image of point C under a dilation about the origin (0,0) with a scale factor of 1/2

Mathematics

1 answer:

yuradex [85]4 years ago

6 0

Answer:

See Attachment for graph

Step-by-step explanation:

Given

Point C

Required

Plot C when dilated by 1/2

First, we have to determine the coordinates of point C

From the attached graph;

$C = (0,6)$

Next, is to determine the new point when dilated;

This is calculated as thus;

$New\ Point = Old\ Point * Scale\ Factor$

$C' = (0,6) * \frac{1}{2}$

Expand the bracket

$C' = (0 * \frac{1}{2}, 6* \frac{1}{2})$

$C' = (0, \frac{6}{2})$

$C' = (0, 3)$

This implies that C' will be plotted at x =0 and y = 3

(See attached for point C')

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2 years ago

Line 1: 2x-3y>12

nata0808 [166]

Answer:

The graph of this line i.e. $2x-3y>12$ should be BELOW the DOTTED line as $y$ involves < symbol.
The graph of this line i.e. $y>-2x+5$ should be ABOVE the DOTTED line as it involves > symbol.
The correct graph for line 1 and line 2 is shown in attached figure.

Step-by-step explanation:

If the inequality involves < or >, then the graph of the equation involves a dotted line.
If the inequality involves ≤ or ≥, then the graph of the equation involves a solid line.

Considering the line 1

$2x-3y>12$

Solving line 1

$2x-3y>12$

$-3y>12-2x$

$3y$

$y$

As $y$ involves < symbol, so the graph of this line should be BELOW the DOTTED line.

But, as you can see that there is an error in the graph. As the graph of $y$ is being shown ABOVE the SOLID line.

Therefore, the graph of this line i.e. $y$ should be BELOW the DOTTED line as it involves < symbol.

Considering the line 2

$y>-2x+5$

As $y>-2x+5$ involves > symbol, so the graph of this line should be ABOVE the DOTTED line.

But, as you can see that there is an error in the graph. As the graph of $y>-2x+5$ is being shown ABOVE the SOLID line.

Therefore, the graph of this line i.e. $y>-2x+5$ should be ABOVE the DOTTED line as it involves > symbol.

The correct graph for line 1 i.e. $2x-3y>12$ and line 2 i.e. $y>-2x+5$ is shown in attached figure.

From the attached graph, it is shown that only (5, -2) satisfies the both inequalities. So, (5, -2) is the correct solution for the given inequalities.

Solution Verification:

Putting (5, -2) in line 1 and line 2

For line 1:

2x - 3y > 12 ⇒ 2(5) - 3(-2) > 12 ⇒ 10 + 6 > 12 ⇒ 16 > 12 which is true.

For line 2:

y > -2x + 5 ⇒ -2 > -2(5) + 5 ⇒ -2 > -10 + 5 ⇒ -2 > -5 which is true.

So, (5, -2) is IN the solution for line 1 and line 2

Putting (-1, -1) in line 1 and line 2

For line 1:

2x - 3y > 12 ⇒ 2(-1) - 3(-1) > 12 ⇒ -2 + 3 > 12 ⇒ 1 > 12 which is false.

For line 2:

y > -2x + 5 ⇒ -1 > -2(-1) + 5 ⇒ -1 > 2 + 5 ⇒ -1 > 7 which is false.

So, (-1, -1) is NOT in the solution for line 1 and line 2

Putting (0, 5) in line 1 and line 2

For line 1:

2x - 3y > 12 ⇒ 2(0) - 3(5) > 12 ⇒ 0 - 15 > 12 ⇒ -15 > 12 which is false.

For line 2:

y > -2x + 5 ⇒ 5 > -2(0) + 5 ⇒ 5 > 0 + 5 ⇒ 5 > 5 which is false.

So, (0, 5) is NOT in the solution for line 1 and line 2

Keywords: inequality, solution, graph, dotted line, solid line

Learn more about inequality solution from brainly.com/question/12036085

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4 0

4 years ago